Applying the Hardy-Weinberg equation

Voiceover: Let's stick with this idea, the simplification, that there's a gene for eye color, and it only comes with two variants. It has the dominant variant, which codes for brown eye color, and it has the recessive variant, which codes for blue eye color. So if either one of your alleles is this capital B, you're going to have brown eyes, the only way to have blue eyes is to have a lower case, is to be homozygous for the recessive allele. Now let's say that in a population, it's a large population, one that meets all the Hardy-Weinberg Equilibrium assumptions, let's say that you were to observe that nine percent of this population has blue eyes. So now we're talking about the phenotype. You can actually observe that they have blue eyes. Based on this, can we figure out p, which is the frequency of the dominant allele. Can we figure this out? And can we figure out q, which is the frequency of the recessive allele, can we figure that out as well? I would encourage you to pause this video and based on what we saw of the Hardy-Weinberg Equation, can we figure these things out, given this information? Well let's revisit the Hardy-Weinberg equation. We've worked it out in a previous video, but I'll rewrite it right now. It says, the allele frequency for the dominant allele frequency squared, plus two times the dominant allele frequency times the recessive allele frequency, plus the recessive allele frequency squared, is equal to one. And we saw that this just comes from the idea that p plus q is going to be equal to one. There is a 100 percent chance, if you were to randomly pick a gene, that it's one of these two variants. Now when we say nine percent has blue eyes, what does that mean? Well the only way to have blue eyes is if your genotype is homozygous recessive. Because if you have a capital B in here then you're going to have brown eyes. So we can say that nine percent also has this genotype. Or you can say that the frequency in the population of this genotype is nine percent. But we've already seen, that's exactly what this term right over here is. That's this q squared term. This is the probability, one way to think about it, of getting, q of course is the frequency of the recessive allele, now you could view this as the probability of getting two of the recessive alleles. In your population, it's going to be nine percent. So we could say q squared is equal to nine percent. Or another way to think about it, this term over here is nine percent, or 0.09. Nine percent has this genotype, that's what this tells us right over here. So then we can solve for q. If q squared, I'll write it as a decimal, 0.09, that means that q is going to be the square root of 0.09, which is equal to 0.3. Just like that, we were able to figure out the allele frequency of the recessive allele. And I could write that as a percentage, 0.3 or 30 percent, if you were looking at the genes in the population, 30 percent express our code for the recessive allele, or the recessive variant. Based on that, we can figure out what percentage code for the dominant variant. The rest of the genes must code for the dominant one, because we're assuming there's only two of them. P plus q equals 100 percent, or p plus q is equal to one. So this must be 70 percent. So just based on that, we can kind of dig a little bit deeper here. So what is p squared? P squared is going to be 70 percent squared, or 0.7 squared. So this right over here is 0.7 squared, which is 0.49. So one way to think about it is, based on this, and once again, it's a simple equation, but these really neat ideas are starting to pop out of it based on just this information. We're now able to say that 49 percent of the population is going to have a genotype of capital B, they're going to be homozygous dominant. And then we can figure out this right over here. Two times p times q, that's going to be two times 0.7, times 0.3. So let's see, that's going to be two times 0.21, so this right over here is going to be 0.42. Or another way to think about it is, 42 percent of this population is going to have the genotype upper case B and lower case b. And you see they all add up. 49 percent plus 42 percent is 91 percent, plus nine percent all adds up to 100 percent. So you get a little bit of information here, and based on what we know about allele frequencies, making a few assumptions, we're able to get a lot more knowledge about this population. And this is actually very useful in real life, when people think about, say, a recessive allele that might cause some type of a disease, based on the incidents of that disease, people can start to think about, "What percentage of the population is a carrier?" Say they're heterzygotes for that disease. So this is actually very useful in real life.